Any of the FastTech modules would work great. IMO, the 50mW version is worth the extra couple dollars but its obviously up to you. As long as you use your head you would basically be safe with any 532nm laser. The main reason being they are so insanely bright to human eyes that you would know instantly if it was too bright to look at. The wavelengths that are not very visible to your eyes like 405nm, 445nm, 660nm are far more dangerous because they can be many times more powerful yet look dimmer.
As for the law, if you built the laser on batteries but didn't put the batteries inside the case with your module/heatsink and instead had them on a wire like 6+ inches long in a separate box and made the cable capable of being plugged and unplugged that would not be a handheld. The whole point would be that it would be too large to fit in a pocket and used with one hand.
A laser based off a wall adapter is not a bad idea though but I would suggest using higher grade components and the price would go up a little. I would get a wall adapter capable of about 9V 1A and then get a constant current constant voltage buck driver and use that to set exactly what you are feeding the module. That way you know exactly what it is receiving. Here is one of the drivers I am talking about and have several of:
DC DC Buck Converter Module LM2596 Constant Current Voltage Adjustable Module | eBay
You said you don't have a multimeter? I my honest opinion(not trying to be mean just being honest), if you are not willing to buy even a cheap multimeter, this is very much not the right hobby for you. That's one of the most basic and essential tools for anyone doing anything with electricity. Here is a multimeter I have bought and used before and it worked amazingly well:
Buy 3.0" LCD Handheld Digital Multimeter (Voltage + Current + Resistance + Temperature / 1*6F22)